Question 35
Integers $a$, $b$, $c$ and $n$ are given such that $1 \le a \lt b \lt c \le n$. Juku and Miku play the following game on a strip of size $1 \times n$: In the beginning, squares number $a$, $b$, $c$ contain one piece each, whereby the squares are numbered from the right to the left by consecutive integers starting from $1$. On one's move, each player chooses one piece out of these three and shifts it one or more squares to the right. However, it is not allowed to move a piece to a square that contains another piece or jump over such a square; one also must not move a piece off the strip. Players move by turns, with Juku moving first. The player who cannot move loses. Which player can win regardless of the opponent's play?